Using a Vitali covering argument one can find the disjoint subset \(\lbrace \tilde{Q}_1,\ldots ,\tilde{Q}_k\rbrace \)  of \(\lbrace Q_1,\ldots , Q_n\rbrace \)  satisfying \(K\subset \bigcup ^k_{j=1}\tilde{Q_j}^*\)  (see the proof of Theorem 3.3.2 of [1]}). To measure \(|K|\)  we compute the ratio \(\frac{|\tilde{Q_j}^*|}{|\tilde{Q_j}|}\) .
For \(Q_j=(t-\frac{r^2}{2},t+\frac{r^2}{2})\times (x^1-r,x^1+r)\times B^{\prime }_r(x^{\prime })\)  we have
\(\frac{|\tilde{Q_j}^*|}{|\tilde{Q_j}|}=3^d\cdot \frac{\phi (x+3r)-\phi ((x-3r)\vee 0)}{\phi (x+r)-\phi (x-r)},\nonumber \) 
